Question

Choose an equivalent system of equations to the following system: fx + gy = h qx + ry = s.

Answer 1

[AI-generated answer — Bot]

A. fx + gy = h; qx - ry = -s

B. fx - gy = -h; qx + ry = s
C. fx - gy = h; qx - ry = s
D. fx + gy = -h; qx - ry = -s

B. fx - gy = -h; qx + ry = s

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find an equivalent system of equations to the given system, we can use the method of substitution.

Start with the original system:
fx + gy = h (Equation 1)
qx + ry = s (Equation 2)

To eliminate one variable, let's solve Equation 1 for x and substitute it into Equation 2:

From Equation 1, we have:
fx = h - gy (rearranging the terms)

Solving for x, we get:
x = (h - gy) / f (dividing both sides by f)

Substituting this value of x into Equation 2, we get:
(q * (h - gy) / f) + ry = s (substituting x into Equation 2)

Now, let's simplify this equation:

(qh - qgy + rfy) / f = s (expanding the equation)

Multiplying both sides of the equation by f to eliminate the fraction, we have:
qh - qgy + rfy = fs (multiplying through by f)

Rearranging the terms, we get:
-qgy + rfy = fs - qh (rearranging terms)

We can further simplify this equation by factoring out the common factor of y:
y(-qg + rf) = fs - qh (factoring out the common factor)

Finally, divide both sides of the equation by (-qg + rf) to solve for y:

y = (fs - qh) / (-qg + rf)

Substituting this value of y back into Equation 1, we can solve for x:

fx + g((fs - qh) / (-qg + rf)) = h (substituting y into Equation 1)

Now, we have an equivalent system of equations:

x = (h - gy) / f
y = (fs - qh) / (-qg + rf)